Comparative study on model-scale sloshing tests

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ORIGINAL ARTICLEComparative study on model-scale sloshing testsSang-Yeob Kim •Kyong-Hwan Kim •Yonghwan KimReceived:26March 2011/Accepted:18September 2011/Published online:1November 2011ÓJASNAOE 2011Abstract This paper considers a comparative study on model-scale sloshing tests.There are two primary scopes of this study:the comparison of sloshing pressure measured in 1/50-scale model tests at Seoul National University (SNU)with (1)the data measured at the other facility for the same model,and (2)the data measured on a smaller scale model.For the comparative study,model tanks are excited with the same irregular motions with Froude scale,and sloshing pressure signals are measured at the same locations.The statistical quantities of 1/50-scale model tests are compared with those of other facility and 1/70-scale model tests.In this study,it is found that peak pressure measured at SNU are slightly lower than those of other facility,and this difference may be due to different sensor types and sensing diameters.Keywords Sloshing experiment ÁScaled model test ÁImpact pressure ÁComparative study1IntroductionThe capacity of 138,000–145,000m 3was the most popular in the LNG carrier (LNGC)market from 1970s to 1990s.From the beginning of the 2000s,the construction of larger LNGC has been dramatically increased,and LNGC with capacity over 180,000m 3appeared in the late 2000s.Although the size of LNGC has been dramatically increased,the number of cargo is still four or five.Suchunbalance can result in the significant increase of sloshing loads on liquefied gas tanks.Despite a lot of previous theoretical and computational efforts to predict sloshing pressure,a model-scale test is still considered the most reliable approach for practical purposes.Because of this reason,in the last decade,very systematic methodologies or concepts for the experimental assessment of sloshing loads have been studied [1,2],and a few large experimental facilities have been built for prac-tical model tests.During the last 2years,an experimental system for sloshing has been also being equipped in Seoul National University (SNU)[3].Currently,there are two motion platforms in SNU:a mid-size platform of 4ton capacity and a small-size platform of 1ton capacity.This study primarily aims at the comparison of two existing facilities.Since existing facilities have different motion platforms and pressure measurement systems,the comparison of experimental results under the same excita-tion conditions is very meaningful and important for checking the consistence of the results.In this study,a 1/50-scale tank model with existing experimental data measured at the other experimental facility is chosen for such com-parative study,and the sloshing experiment is carried at SNU facility for the same tank model.The pressure signals of 5-h time window in real scale are measured and statistical analysis are carried out for peak pressures.Those results are compared with other facility’s results,and their differences are observed.This study is extended to a series of experiment for a 1/70-scale model with the same shape,and experimental results are compared with those of the 1/50-scale model.In this experiment,excitation motions are properly scaled by using the 1/50-scale test cases in order to apply the same motion characteristics,but the same pressure sensors are equipped.That is,the sizes of sensing area are different if those areS.-Y.Kim ÁK.-H.Kim ÁY.Kim (&)Department of Naval Architecture and Ocean Engineering,Seoul National University,588,Gwanak-ro,Gwanak-gu,Seoul 151-744,Koreae-mail:yhwankim@snu.ac.krJ Mar Sci Technol (2012)17:47–58DOI 10.1007/s00773-011-0144-zscaled up to real-ship size.Generally,to get consistency in scaled model tests,the sensing diameter of pressure sensors should be properly scaled for different model scales.How-ever,in the actual situation(s),finding a set of properly-scaled sensors is very hard.Therefore,it is very important to know the effects of the sensor size.In this paper,some key findings from this comparative study are discussed.2Experimental setupThis study has two primary objectives:comparison of sloshing loads measured(1)at two different facilities for the same tank model and excitation condition,and(2)for different scale models under the same excitation motion. To this end,two motion platforms in Seoul National Uni-versity are used.The motion platforms are hexapod type with six actuators,as shown in Fig.1.The capacities of the platforms are4and1ton,and both can generate6-DOF regular and irregular motions.The two models considered in these tests are the1/50and 1/70scaled tanks of a140,000LNGC.The1/50-scale model is tested by using the motion platform of4-ton capacity, while the other is installed on the platform of1-ton capacity. The tank models are made of transparent acrylic plates.The thicknesses of the plates are20mm in the1/70-scale tank and35mm in the1/50-scale tank,respectively.The media filled inside the tanks are air and water.Figure2shows the two different scaled tank models and Fig.3shows the dimensions of1/50-scale model.The dimensions of tank models are decided by Hyundai Heavy Industry(HHI).Sloshing pressure is measured by using211B5sensors which are integrated circuit piezoelectric(ICP)-type sen-sors made by Kistler.Sensor diameter is5.54mmandMid-size (4 ton) b Small-size (1 ton)aFig.16-DOF motionplatforms1/50-scale 1/70-scalebaFig.2Tank modelsmaximum pressure range is 7bars.The 1/50-scale tests reproduce the existing experiments performed at MARINTEK,hereafter named as the other facility in the text.In this case pressure sensors with the sensing diameter of 2mm,manufactured by Kulite Co.,were used.There-fore,there is a strong possibility that the difference of two sensors,particularly sensor diameters,can be the primary source of the discrepancy of the data measured at two facilities.The positions of the pressure sensors are shown in Fig.4.Sensor positions are chosen to be consistent between the two tests.In recent experimental studies for sloshing,sampling the rate of 20kHz is widely applied [4,5].Most recently,Nitin et al.[6]carried out a comparative experiment with varying sampling rates from 20to 100kHz and suggested20–40kHz as a reasonable range of sampling rate.In this study,the sampling rate of pressure measurement is set to 20kHz in both the 1/50and 1/70scale tests.It means,sampling rate is not exactly scaled.For better consistency,the sampling rate should be scaled properly,and such scaling will be considered in future work.Table 1summarizes the test conditions of the present experiment.In this study,five filling levels are considered,and one sea-state per each filling condition is applied.Although the motion platforms can generate 6-DOF motions,4-DOF motions are applied in the present study,since the previous experiment at the other facility has been carried under 4-DOF excitation.The input motion signals for the excitation platform are exactly the same to those applied at the other facility,and pressure signals are95% and 70% filling 50% filling30% filling10% fillinga b c d Fig.4Positions of pressure sensors (darker locations indicate the activesensors)Fig.3Dimensions of 1/50-scale modelmeasured during 5h in real time In addition,Froude scaling is used to scale the motion and pressure up or down.3Analysis methodIn early times,Mathiesen [7]and Gran [8]introduced pioneering researches on a statistical approach to predict extreme pressure values.Mathiesen introduced theapplication of Weibull distribution for a set of sampled peak pressure values.Gran compared the goodness of fit-ting to Weibull and Fretchet distributions,and this study has been the theoretical background of many researches afterward [9–11].In this paper,statistical analysis is carried out to com-pare the test results.The threshold pressure and sampling time-interval for peak samples are set to 5.0kPa and 0.2s in the 1/50-scale tests,and 3.6kPa and 0.17s in theSNUOther facilitya b Fig.5Sloshing impact signals from two facilities:10%filling,channel no.=18Table 1Experimental conditions in real scale:L (tank length),H (tank height)DescriptionShip model HHI 140K LNG carrier Filling level 10%(0.19L a )30%(0.39H )50%(0.59H )70%(0.79H )95%(0.959H )Sea-stateH s =7.01m,T z =6.0sH s =12.82m,T z =8.5sWave heading angle (°)90030Simulation time5ha10%filling:water depth =0.19L ,all others are with respect to Ha SNUb Other facilityFig.6Sloshing impact signals from two facilities:95%filling,channel no.=1395% filling: SNU95% filling: Other facility70% filling: SNUc b aFig.7Pressure signals of three largest sloshing impacts measured at different facilities70% filling: Other facilitye d 30% filling: SNUf 30% filling: Other facilityFig.7continued1/70-scale tests.It was presented that statistical results are not very sensitive to the threshold pressure and sampling time-interval as long as they are not very small or large [12].As a temporal parameter of sloshing-induced peaks,rising time is considered.In this study,rising time is defined as follows:T rise ¼2t P max Àt ð0:5P max Þup -crossing ÀÁ:ð1Þwhere t P max is the time when peak pressure P max occurs,and t ð0:5P max Þup -crossing is up-crossing time when pressure becomes 0.5P max .The average of the (1/n )largest peaks and probable extreme pressure are observed for the comparison of sta-tistical properties.Particularly,three-parameter Weibull and Pareto distribution functions are considered to repre-sent the extreme distribution function of peak pressures.The cumulative distribution function of three-parameter Weibull distribution can be written as F ðx Þ¼1Àexp Àðx Àd Þ=b ½ c ðÞð2Þwhere d is the location parameter,b is a scale parameter,and c is a shape parameter.Here,x should be larger than the location parameter,d .To estimate these three parameters,the method of moments can be applied.In this method,the parameters are estimated by matching thefirst three model moments,mean (l ),variance (r 2),and skewness (c 1)with corresponding sample moments.Themean,variance and skewness are given byl ¼b C 1þ1cþdð3Þr 2¼b 2C 1þ2c ÀC 21þ1c!ð4Þc 1¼C 1þ3c À3C 1þ1c C 1þ2c þ2C 31þ1cC 1þ2c ÀC 21þ1ch i 3=2ð5Þwhere C is the Gamma function.In order to establish a model which gives a better fit to the larger values in the tail,a peak-over-threshold (POT)method can be utilized for fitting the sample data.The POT method uses only the data which exceeds a certain threshold value,and the cumulative distribution function of peaks is described asF ðx Þ¼F X ðx Þ1ÀF ðu Þ½ þF ðu Þð6Þwhere u is the threshold value,and F X (x )is the distribution of pressure peaks over threshold.x should be larger than95% filling 70% filling30% filling 10% fillingc a bd Fig.8Comparison of the scatter diagrams of sloshing peaks measured at different facilities (from all pressure sensors)the threshold value.According to Pickands [13],F X (x )asymptotically follows the generalized Pareto distribution model,and the cumulative distribution function of this model is given byG ðx Þ¼1À1þcx =k ðÞÀ1=c if c ¼01Àexp Àx =k ðÞif c ¼0&ð7Þwhere the range of x is 0\x \?for c C 0and0\x \-c /k for c \0.k is a scale parameter and c is a shape parameter.To estimate the parameters,the method of moments can be applied.The mean and variance are given by Bury [14]as l ¼k 1Àcð8Þr 2¼k 2ð1À2c Þð1Àc Þð9Þ4Experimental resultsThe representative sloshing pressure signals measured at two different facilities are presented in Figs.5and 6.Because of the nonlinearity of sloshing phenomena,the same sloshing peaks cannot be expected at the same time between the two cases.However,the patterns of impact signal can be compared.Figure 5shows the pressure sig-nals measured on a port-side wall near a lower chamfer in the 10%filling condition.In the results of SNU,pressure values after the impact is slightly higher than zero,while the pressure becomes lower than zero in the results of other facility.This tendency is shown in most pressure signals of the two tests.Such difference seems to be due to the dif-ference of sensor types.Figure 6shows the examples of impact signals measured at the tank top in the 95%filling level,and the oscillations seem to be caused by air bubbles or large air pockets.In this condition,the pressure patterns of the two tests look similar.Figure 7shows the pressure signals of three largest sloshing peaks among the all channels in three filling lev-els.Locations where the largest sloshing peak measured show good agreement between two tests,and the signals look similar in all the filling cases although the magnitudes of peak pressures shows some differences.This comparison proves that pressure measurements at the two test facilities are comparable.The temporal evolution and peak value of the impacts are the two main issues of sloshing-induced loads.Figure 8shows the scatter diagrams of sloshing peaks in different filling levels.x and y axes represent rising time and peak pressure,respectively.These scatter diagrams show fair agreement.In terms of rising time the best agreement seems to occur for 70%filling while in terms of maximum pressure peak it seems to occur for 30%filling.The most scattered tendency can be observed in the 30%filling condition,while the most concentrated distribution shows in the 70%filling condition.It should be noticed that,in the 70%filling,the rising times of all peaks are less than 1.5ms.Figure 9shows the bar-type plots of pressure peaks measured at the two different facilities.The values in these plots are from the pressure signals of all sensors.It can be found that the magnitudes of pressure peaks look similar except for one or two extraordinary high peaks.There is one large peak in the 50%filling case,which was measured at the other facility.This peak can give a significant effect to the statistical results and disturb an appropriate com-parison of the two tests.In addition,it should be mentioned that the numbers of sloshing peaks measured in the 50%filling level are relatively small when compared to those of other filling level tests,indicating that sloshing flow is not violent as much as other filling conditions.95% filling50% filling30% fillinga cb Fig.9Comparison of time-histories of sloshing peak measured at different facilities (from all pressure sensors)The exceedance probability diagrams for the measured sloshing peaks of the two tests are shown in Fig.10.In all filling levels,the Weibull distributions of other facility’sresults are more weighted toward the right than those of SNU.It means that the most probable extreme pressures of the other facility are larger than those of SNU considering the same cumulative probability.The statistical results of the present 1/50-scale tests are summarized in Fig.11which shows the ratios of the peak pressures measured at SNU with respect to those measured at the other facility.As shown in this comparison,the ratios are smaller than 1.0in all filling levels and the overall ratios are close to 0.8.This means that the sloshing peaks measured at SNU are relatively smaller than those mea-sured at the other facility.In the case of the 95%filling condition,the ratio is close to 1.0,while in the case of the 70%filling condition,the ratio of 3-h extreme values is close to 0.6.When consid-ering the different sensor diameters of pressure sensors,this trend can be acceptable.In most cases except the 30%condition,the ratios for the 3-h extreme pressures are smaller than those of averaged 1/10largest values.It means that,as a higher cumulative probability is considered,the gap between the corresponding extreme pressures of the tests at two facilities becomes bigger.The number of sloshing peaks measured in the different tests is reported in Table rge numbers of peak samples do not guarantee the good agreement between the results of the two facilities.However,if the number of peak samplesTable 2Numbers of measured sloshing peaks from the tests con-ducted by two different facilities (accumulated from all pressure sensors)Filling level 10%30%50%70%95%SNU 19773993159654Other facility16075612734483995% filling 70% filling30% filling 10% fillinga b c d Fig.10Exceedanceprobabilities for sloshing peaks (from all pressuresensors)Fig.11Statistical results:ratio of peak pressure measured at SNU’s result to that of other facility,data from all sensorsis small,statistical results get less confidence and have more uncertainty.By cross-examining results in Table 2with those in Figs.11and 12,the tests with less agreement have relatively smaller pressure impact and less number of sloshing peaks.The ratios of the sloshing pressure at each tank face are compared in Fig.12.Naturally,the statistical results of the pressure peaks are dependent on the tank face.For exam-ple,in the 95%filling condition,the ratio at the port upperchamfer is very close to 1.0,while the ratio at the forward bulkhead is lower than 0.5.A positive fact observed from the present comparison is that the results between the two facilities show good correspondence in the regions where high impact pressures occur, e.g.the port-side upper chamfer in 95,50and 30%fillings,tank top in 70%filling,and port-side wall in 10%filling.As mentioned,it is very possible that the main source of the difference between the results of the two facilities is the95% filling 70% filling30% filling10% fillinga b c d Fig.13Statistical properties of tests in real scale (from all pressure sensors)95% filling 70% filling30% filling10% fillingb acd Fig.12Statistical results:ratio of peak pressure measured at SNU’s result to that of other facility,data from the sensors at each tank facedifferent diameters of two sensors.To examine further the effects of the sensor diameter,a series of1/70-scale model test are carried out with the sensors which are used for the 1/50-scale model tests.Pressure sensors should be properly scaled up or down as the model scale changes.However,it is not easy to change the size of sensor in a real situation. Furthermore,based on the experimental experience and/or due to some reasons,each facility has a preference on dynamic pressure sensors.So,like the present case,two different facilities use difference sensors.Figure13compares the real-scaled statistical properties of three cases,i.e.the impact pressures conducted at dif-ferent test facilities with different model scales.In this study,Froude scaling without density correction is used to translate the pressures of the model scale to those of the real scale.The application of Froude scaling can be an issue in this comparison,but this discussion will not be included in this paper.From the comparison of the statistical results of the 1/50-scale and1/70-scale model tests at SNU,it can be found that the statistical results of the1/70-scale tests show a fair agreement to those of the1/50-scale test in allfilling levels.It means that the effect of the pressure-sensor size with a different scale model test may be highly significant. However,for more solid conclusion,a systematic study with proper scaling for the sensor size,sampling frequency, and test material(e.g.liquid and gas)is essential.5ConclusionsBased on the present comparative studies,the following conclusions are introduced:•In the1/50-scale tests,sloshing loads measured at SNU are smaller than those of measured at the other facility.Such difference seems to be caused mainly by the difference of the sensing diameter and type of pressure sensors.•The difference of the sloshing pressure at70%is higher than any otherfilling conditions.At thisfilling,pressure peaks show narrower rising time than at the other cases, which means that impact pressures are spiky and consequently more localized.Then,the magnitude of the peak pressure can be sensitive to the sensor diameter.•The difference between local sloshing impact pressures measured at SNU and other facility is slightly depen-dent on the measuring positions.It is hard to conclude the reason of such difference,but overall trends are acceptable.•The statistical results of the1/50-and1/70-scale tests show acceptable agreement when Froude scaling isapplied.However,the results of the1/70-scale tests are still smaller than those of the1/50-scale measured at the other facility.•The sloshing impact pressure is sensitive to the type of the pressure sensor.In order to get more reliable conclusions,various types of pressure sensors should be tested and repetition tests should be carried out to reduce the uncertainty of sloshing experiments.Fur-thermore,a large scale test is recommended to inves-tigate the scale effect.Acknowledgments This study was mainly sponsored by Daewoo Shipbuilding and Marine Engineering Co.,Samsung Heavy Industry, STX Offshore&Ship building Co.,Hanjin Transportation Manage-ment System,Hyundai Heavy Industry,and Ministry of Knowledge Economy(MKE)in Korea.A part of the research has been supported also by The LRET-Funded Research Center at SNU for FSI (LRETC).Their supports are greatly appreciated.Authors also thank the administrative support of Engineering Research Institute and RIMSE of Seoul National University.References1.Graczyk M,Moan T,Rognebakke O(2006)Probabilistic analysisof characteristic pressure for LNG tanks.J Offshore Mech Arct Eng128:133–1442.Kuo JF,Campbell RB,Ding Z,Hoie SM,Rinehart AJ,Sands-tro¨m,RE,Yung TW,Greer MN,Danaczko MA(2009)LNG tank sloshing assessment methodology—the new generation.In:Pro-ceedings of the19th international offshore and polar engineering conference,ISOPE,Osaka,Japan3.Advanced Marine Technology(2010)Development of large scalesloshing experiment facilities.AMEC Project Report,Seoul National University,Seoul,Korea4.Kim HI,Kwon SH,Park JS,Lee KH,Jeon SS,Jung JH,Ryu MC,Hwang YS(2009)An experimental investigation of hydrody-namic impact on2-D LNGC models.In:Proceedings of the19th international offshore and polar engineering conference,ISOPE, Osaka,Japan5.Maillard S,Brosset L(2009)Influence of density ratio betweenliquid and gas on sloshing model test results.In:Proceedings of the19th international offshore and polar engineering conference, ISOPE,Osaka,Japan6.Nitin R,Tam T,Krish T,Dominique R,Robert KM,Timothy F(2010)The effect of sampling rate on the statistics of impact pressure.In:Proceedings of the29th international conference on ocean,offshore and arctic engineering,OMAE,Shanghai,China 7.Mathiesen J(1976)Sloshing loads due to random pitching.NorMarit Res4(3):2–138.Gran S(1981)Statistical distributions of local impact pressures inliquid sloshing.Nor Marit Res9(2):2–129.American Bureau of Shipping(2006)Guidance notes on strengthassessment of membrane-type LNG carriers.Guidance note (updated in2009),Houston,USA10.Det Norske Veritas(2006)Sloshing analysis of LNG membranetanks.Classification notes,Oslo,Norway11.Ryu MC,Jung JH,Jeon SS,Hwang YS,Han SK,Kim YS,ChoTI,Kwon SH(2009)Reference load for a conventional138K CBM LNG carrier in a comparative approach.In:Proceedings of the28th international conference on ocean,offshore and arctic engineering,OMAE,Honolulu,Hawaii,USA12312.Kim Y,Kim SY,Yoo WJ(2010)Statistical evaluation of localimpact pressures in sloshing.In:Proceedings of the20th inter-national offshore and polar engineering conference,ISOPE, Beijing,China 13.Pickands J III(1975)Statistical inference using extreme orderstatistics.Ann Stat3(1):119–13114.Bury KV(1975)Statistical models in applied science.Wiley,New York123。